Shiozaki Toru, Hirao Kimihiko, Hirata So
Department of Applied Chemistry, Graduate School of Engineering, The University of Tokyo, Tokyo 113-8656, Japan.
J Chem Phys. 2007 Jun 28;126(24):244106. doi: 10.1063/1.2741262.
Second- and third-order perturbation corrections to equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) incorporating excited configurations in the space of triples [EOM-CCSD(2)T and (3)T] or in the space of triples and quadruples [EOM-CCSD(2)TQ] have been implemented. Their ground-state counterparts--third-order corrections to coupled-cluster singles and doubles (CCSD) in the space of triples [CCSD(3)T] or in the space of triples and quadruples [CCSD(3)TQ]--have also been implemented and assessed. It has been shown that a straightforward application of the Rayleigh-Schrodinger perturbation theory leads to perturbation corrections to total energies of excited states that lack the correct size dependence. Approximations have been introduced to the perturbation corrections to arrive at EOM-CCSD(2)T, (3)T, and (2)TQ that provide size-intensive excitation energies at a noniterative O(n(7)), O(n(8)), and O(n(9)) cost (n is the number of orbitals) and CCSD(3)T and (3)TQ size-extensive total energies at a noniterative O(n(8)) and O(n(10)) cost. All the implementations are parallel executable, applicable to open and closed shells, and take into account spin and real Abelian point-group symmetries. For excited states, they form a systematically more accurate series, CCSD<CCSD(2)T<CCSD(2)TQ<CCSD(3)T<CCSDT, with the second- and third-order corrections capturing typically approximately 80% and 100% of such effects, when those effects are large (>1 eV) and the ground-state wave function has single-determinant character. In other cases, however, the corrections tend to overestimate the triples and quadruples effects, the origin of which is discussed. For ground states, the third-order corrections lead to a rather small improvement over the highly effective second-order corrections [CCSD(2)T and (2)TQ], which is a manifestation of the staircase convergence of perturbation series.
已实现对运动方程耦合簇单双激发态（EOM - CCSD）的二阶和三阶微扰修正，这些修正纳入了三重态空间中的激发组态[EOM - CCSD(2)T和(3)T]或三重态和四重态空间中的激发组态[EOM - CCSD(2)TQ]。它们的基态对应物——三重态空间[CCSD(3)T]或三重态和四重态空间[CCSD(3)TQ]中耦合簇单双激发态（CCSD）的三阶修正——也已实现并进行了评估。结果表明，直接应用瑞利 - 薛定谔微扰理论会导致对激发态总能量的微扰修正缺乏正确的规模依赖性。已对微扰修正引入近似，以得到EOM - CCSD(2)T、(3)T和(2)TQ，它们能以非迭代的O(n(7))、O(n(8))和O(n(9))成本（n为轨道数）提供规模密集型激发能，以及以非迭代的O(n(8))和O(n(10))成本提供CCSD(3)T和(3)TQ的规模扩展总能量。所有实现都是并行可执行的，适用于开壳层和闭壳层，并考虑了自旋和实阿贝尔点群对称性。对于激发态，它们形成了一个系统上更精确的序列，CCSD < CCSD(2)T < CCSD(2)TQ < CCSD(3)T < CCSDT，当这些效应较大（>1 eV）且基态波函数具有单行列式特征时，二阶和三阶修正通常分别捕获约80%和100%的此类效应。然而，在其他情况下，这些修正往往会高估三重态和四重态效应，并对其起源进行了讨论。对于基态，三阶修正相对于高效的二阶修正[CCSD(2)T和(2)TQ]带来的改进相当小，这是微扰级数阶梯式收敛的一种表现。
